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A343424
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Numbers k such that sopfr((k-1)!) is divisible by k, where sopfr(k) = A001414(k) = sum of primes, with repetition, dividing k.
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1
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1, 2, 45, 53, 177, 436, 1239, 3651, 6463, 6869, 10753, 19450, 29721, 33289, 88907, 93682, 1137232, 1516121, 4361271, 9428534, 43778664, 74738670, 271442366, 775223371, 835126289, 1736463189, 3088442241, 5054888590, 11184483614, 16993011938, 30788570768, 33342871740
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OFFSET
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1,2
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COMMENTS
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See A025281(k-1) for the values of sopfr((k-1)!).
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LINKS
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EXAMPLE
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45 is a term as sopfr(44!) = 585 which is divisible by 45.
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MATHEMATICA
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sopfr[0] = sopfr[1] = 0; sopfr[n_] := Plus @@ Times @@@ FactorInteger[n]; sum = 0; s = {}; Do[sum += sopfr[n]; If[Divisible[sum, n + 1], AppendTo[s, n + 1]], {n, 0, 10^6}]; s (* Amiram Eldar, May 06 2021 *)
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PROG
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(PARI) sopfr(n) = (n=factor(n))[, 1]~*n[, 2]; \\ A001414
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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